Overview of this workshop
With recent rapid progresses in theoretical physics, it has been clarified that quantum information theory and gravity theory-- they are apparently different theories at a glance -- are deeply related each other. Profound relations found between these two have attracted great attention in the research areas of quantum information and string theory. The researches are currently achieving explosive growth all over the world, which results in many posts every day in arXiv. Behind these significant developments, there are a lot of important achievements accumulated in quantum information theory and string theory, independently.
In the quantum information theory, one of the most important issues is how to formulate the resources for quantum computing and quantum communication, e.g., quantum entanglement. A measure of quantum entanglement for pure states is defined by the von-Neumann entropy. Generalizations of entanglement measure for mixed states have also been studied by many authors. The theory of such quantum entanglement has significantly developed in these two decades, clarifying what are possible/impossible on the operation of the quantum systems.
Another important issue is to experimentally realize quantum computers. Quantum error-correcting code has been proposed as a solution to the decoherence problem in macroscopic systems. The theory of quantum error correction is interesting not only in view of the practical purpose of realizing quantum computers, but also has intriguing mathematical structure of its own. Since it has a close relationship with the physics of fermion and topological systems, pure theoretical researches are actively carried out as an important theme of theoretical physics. Moreover, it has recently been known that the quantum error-correcting code plays an important role in gravity theory.
In the realization of quantum computers, it is also important to study what problems can be solved quickly. Quantum computing is studied worldwide at present, quantifying the timescales needed to solve the problems of concern. By using a new scheme "measurement-based quantum computing", it analyzes computational capability of quantum multi-body systems. In traditional physics, quantum multi-body systems are classified from a macroscopic point of view by calculating distribution functions. While in quantum computing, the system is characterized and classified in view of micro-structure, e.g., the computing power when it is used in quantum computation.
In the string theory, -- one of its original aims is to construct the quantum theory of gravity -- the gauge/gravity correspondence was discovered 20 years ago, and many important achievements have followed since then. However, a thorough understanding of the fundamental principle is yet to be achieved. The elucidation of its whole mechanism is regarded as one of the most important issues in the string theory, as the progress along this line may lead to the understanding of the quantum gravity in more realistic universes such as the de Sitter spaces.
Although the original aims of these two research fields, the quantum information theory and the string theory, are completely different, it has been revealed that they are deeply connected with each other through gauge/gravity correspondence. By using the gauge/gravity correspondence, one can calculate the entanglement entropy in quantum field theory as a geometric quantity, namely a surface area. From this fact, it is conjectured that gravity is equivalent to the dynamics of the entanglement in quantum multi-body systems as investigated by many authors. Moreover, the method for analyzing the entanglement entropy has been developed significantly with the help of the progress in the study of quantum field theory.
Furthermore, it has been conjectured that tensor networks may give an explanation of the mechanism how anti-de Sitter space emerges from conformal field theories. Interestingly, we can view tensor networks as a geometry of quantum entanglement and fit nicely with results in gauge/gravity correspondence. Many progresses have been made in this direction until now, such as perfect tensor models and random tensor networks.
Remarkably, the quantum error-correcting codes mentioned above play an important role in the constructions of such tensor models. In fact, it is argued that the relation between gravity and field theories in the gauge/gravity correspondence can be regarded as a version of quantum error-correcting codes. Through detailed studies of these topics, we may reach a complete understanding of the fundamental mechanism of the gauge/gravity correspondence.
In addition, computational complexity is often discussed recently as an interesting measure of complexity of quantum states in the context of the gauge/gravity correspondence. It is expected that it may reveal unknown features of quantum states which cannot be captured by the entanglement entropy. Some calculations have been proposed in the gravity side and the study in the field-theory side has started. There are many problems remained unsolved along this line of research.
Under these circumstances, we believe that it is timely to have comprehensive and intensive discussions on the rapidly expanding frontiers of quantum information and string theory inviting leading experts in the world. Topics covered by the workshop are as follows.
- Resources for quantum computing; quantum entanglement, etc.
- Quantum computing, in particular quantum interactive proof systems, etc.
- Quantum error-correcting codes, fermion and topological systems
- Tensor networks and measurement-based quantum computing
- Quantum supremacy in non-universal quantum computing
- Quantum cryptography protocol; e.g., blind quantum computing, etc.
- Entanglement entropy in quantum field theory
- Relations between gauge/gravity correspondence and entanglement entropy
- New inequalities in quantum gravity theory from quantum information theory
- Fundamental principle of gauge/gravity correspondence and tensor networks
- Connections between gauge/gravity correspondence and quantum error-correcting codes
- Black hole information paradox and quantum information theory
- Complexity of states in quantum field theory and gauge/gravity correspondence